There is an option in gsettings for this, com.canonical.unity-greeter play-ready-soundbut currently isn't working. One simple thing that does work is when on the greeter screen just turn the volume off in the sound indicator. The setting is persistent
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dougApr 21 '12 at 3:26

@doug, thanks. The second and third sentence of your comment don't pertain this answer. I think they should go as separate answer to my question to be more visible.
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KrigeApr 21 '12 at 21:53

I think the answer for changing the sound permanently is currently in moving or removing this file: /usr/share/sounds/ubuntu/stereo/system-ready.ogg. See from this thread --> ubuntuforums.org/…
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e.m.fieldsJun 19 '13 at 18:28

aendruk, I'm in favor of nondestructive solutions when they're available, but up to this point seems to have been none. What is this file? Is this a patch to an existing system application?
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e.m.fieldsAug 29 '13 at 7:38

For Ubuntu 12.04+

LightDM Way

Also known as the FluteFlute Slap, the LightDM Way involves having to logout and on the LightDM Login Screen you can change the volume or even mute the sound.

In the Login Greeter you can see the Volume on the top right. Adjusting the volume there does not affect the volume when the session starts, so you can MUTE the sound in the Greeter without muting the sound when your session starts:

Ubuntu Tweak Way

The Ubuntu Tweak way involves having to download the Ubuntu Tweak app and then disabling the sound from there. Do the following steps and you can do it this way:

well, this turns off the sound after the login, i want to turn off the sound on the login screen
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tomMar 7 '12 at 11:07

@tom - you are correct, I misunderstood your question. To disable or remove the system ready sound (the drum beats) you need to follow the steps in the other posted answers, either one will work.
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Mark RooneyMar 7 '12 at 21:29